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Dynamically Consistent Conditional Choquet Capacities

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  • Robert Kast

    ()

  • André Lapied

Abstract

Preferences of a Decision Maker define a valuation function on future uncertain payoffs. Consistency of this unconditional valuation function with valuation conditional on information arrivals is justified by a no Money Pump argument. A result on the updating of capacities is obtained in a static framework. Then the arguments are developed in a model where the future payoffs are contingents on two components: uncertain states and future dates. We obtain results on updating capacities on the uncertain states and “upstating” capacities (discount factors) on future dates in a special case. These results are shown to violate consequentialism.

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File URL: http://www.icer.it/docs/wp2007/ICERwp20-07.pdf
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Bibliographic Info

Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 20-2007.

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Length: 34 pages
Date of creation: Mar 2007
Date of revision:
Handle: RePEc:icr:wpmath:20-2007

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Related research

Keywords: Comonotonicity; Capacities on product spaces; Updating; Flexibilities;

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References

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  1. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  2. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Alain Chateauneuf & Robert Kast & André Lapied, 2001. "Conditioning Capacities and Choquet Integrals: The Role of Comonotony," Theory and Decision, Springer, vol. 51(2), pages 367-386, December.
  4. Ghirardato, Paolo, 1995. "On Independence For Non-Additive Measures, With a Fubini Theorem," Working Papers 940, California Institute of Technology, Division of the Humanities and Social Sciences.
  5. Hammond, Peter J, 1989. "Consistent Plans, Consequentialism, and Expected Utility," Econometrica, Econometric Society, vol. 57(6), pages 1445-49, November.
  6. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-68, December.
  7. David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
  8. Kreps, David M & Porteus, Evan L, 1979. "Dynamic Choice Theory and Dynamic Programming," Econometrica, Econometric Society, vol. 47(1), pages 91-100, January.
  9. A. Chateauneuf & R. Kast & A. Lapied, 1996. "Choquet Pricing For Financial Markets With Frictions," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 323-330.
  10. Diecidue, Enrico & Wakker, Peter P., 2002. "Dutch books: avoiding strategic and dynamic complications, and a comonotonic extension," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 135-149, March.
  11. De Waegenaere, Anja & Kast, Robert & Lapied, Andre, 2003. "Choquet pricing and equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 359-370, July.
  12. Karni, Edi & Schmeidler, David, 1991. "Atemporal dynamic consistency and expected utility theory," Journal of Economic Theory, Elsevier, vol. 54(2), pages 401-408, August.
  13. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
  14. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
  15. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
  16. Kast, Robert & Lapied, Andre, 2003. "Comonotonic book making and attitudes to uncertainty," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 1-7, August.
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Cited by:
  1. Robert Kast & André Lapied, 2008. "Valuing future cash flows with non separable discount factors and non additive subjective measures: Conditional Choquet Capacities on Time and on Uncertainty," Working Papers 08-09, LAMETA, Universtiy of Montpellier, revised Jun 2008.

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